1. Field of the Invention
The present invention relates to a motor control apparatus for controlling currents flowing through the armatures of a DC brushless motor according to a feedback control process.
2. Description of the Related Art
One conventional method of controlling a DC brushless motor employs a vector control process (hereinafter referred to as xe2x80x9cdq control processxe2x80x9d) which converts a 3-phase (U, V, W) DC brushless motor into an equivalent circuit having a q-axis armature on a q-axis which is aligned with the direction of magnetic fluxes of field systems on the rotor of the motor and a d-axis armature on a d-axis which extends perpendicularly to the q-axis.
A conventional motor control apparatus for carrying out the dq control process is arranged as shown in FIG. 3 of the accompanying drawings. As shown in FIG. 3, a motor control apparatus 50 serves to control currents flowing through the armatures of a DC servomotor 51, and has a U-phase current sensor 52 for detecting a current IU_s flowing through a U-phase armature of the DC servomotor 51 and a W-phase current sensor 53 for detecting a current IW_s flowing through a W-phase armature of the DC servomotor 51.
The currents IU_s, IW_s and an electric angle xcex8 of the rotor of the motor 51 which is detected by a position detecting sensor (resolver or the like) 54 are supplied to a 3-phase/dq converter 55, which outputs an actual current Id_s flowing through the d-axis armature and an actual current Iq_s flowing through the q-axis armature.
The motor control apparatus 50 is supplied with a command value Id_c for the current flowing through the d-axis armature and a command value Iq_c for the current flowing through the q-axis armature. A first subtractor 56 calculates the difference xcex94Id between the command value Id_c and the actual current Id_s, and a second subtractor 57 calculates the difference xcex94Iq between the command value Iq_c and the actual current Iq_s.
A first PI processor 58 and a second PI processor 59 perform a proportional and integral (PI) process to reduce the differences xcex94Id, xcex94Iq, and calculate a command value Vd_c for the voltage applied to the d-axis armature and a command value Vq_c for the voltage applied to the q-axis armature, respectively. The command values Vd_c, Vq_c are supplied to a dq/3-phase converter 60, which converts them into command values VU_c, VV_c, VW_c for the voltages applied to the three-phase (U, V, W) armatures. A power drive unit 61 applies voltages according to the command values VU_c, VV_c, VW_c to the three-phase armatures of the motor 51.
The process carried out by the first PI processor 58 and the second PI processor 59 is expressed by the following equation (1):                               [                      Vd            Vq                    ]                =                  [                                                                                          Kp                    ⁢                                          xe2x80x83                                        ⁢                    Δ                    ⁢                                          xe2x80x83                                        ⁢                    Id                                    +                                      Ki                    ⁢                                          ∫                                              Δ                        ⁢                                                  xe2x80x83                                                ⁢                        Id                        ⁢                                                  ⅆ                          t                                                                                                      +                                      ω                    ⁢                                          xe2x80x83                                        ⁢                    Ke                                                                                                                                            Kp                    ⁢                                          xe2x80x83                                        ⁢                    Δ                    ⁢                                          xe2x80x83                                        ⁢                    Iq                                    +                                      Ki                    ⁢                                          ∫                                              Δ                        ⁢                                                  xe2x80x83                                                ⁢                        Iq                        ⁢                                                  ⅆ                          t                                                                                                                                                  ]                                    (        1        )            
where Vd: the voltage applied to the d-axis armature, Vq: the voltage applied to the q-axis armature, Kp: the proportional gain, Ki: integral gain, xcfx89: the angular velocity of the motor, and Ke: the induced voltage constant.
In the applications of many motors, sufficient stability and responsiveness is achieved by the feedback control process of the above general proportional and integral control system. However, when the motor is operated at high rotational speeds, the motor may operate unstably or the control responsiveness may become insufficient under the control of the general proportional and integral control system.
The primary reason for the above drawbacks is considered to reside in that since the state equation of the proportional and integral control system is given as the following equation (2), when the motor operates at a high rotational speed, interference between the d- and q-axes increases due to the induced voltage generated depending on the angular velocity xcfx89 of the motor, causing the control system to respond in a vibrating fashion.                                           ⅆ                          ⅆ              t                                ⁡                      [                                                            Id                                                                              Iq                                                      ]                          =                              [                                                                                -                                                                  r                        +                        Kp                                            Ld                                                                                                            ω                    ⁢                                          xe2x80x83                                        ⁢                                          Lq                      Ld                                                                                                                                                              -                      ω                                        ⁢                                          Ld                      Lq                                                                                                            -                                                                  r                        +                        Kp                                            Lq                                                                                            ]                    ⁢                      "AutoLeftMatch"                                          [                                                                            Id                                                                                                  Iq                                                                      ]                            -                              [                                                                                                                              Ki                          Ld                                                ⁢                                                  ∫                                                      Id                            ·                                                          ⅆ                              t                                                                                                                                                                                                                                                        Ki                          Lq                                                ⁢                                                  ∫                                                      Iq                            ·                                                          ⅆ                              t                                                                                                                                                                          ]                            -                                                [                                                                                                              r                          Ld                                                                                            0                                                                                                            0                                                                                              -                                                      r                            Lq                                                                                                                                ]                                ⁡                                  [                                                                                    Id_c                                                                                                            Iq_c                                                                              ]                                                                                        (        2        )            
where Id: the current flowing through the d-axis armature, Iq: the current flowing through the q-axis armature, Ld: the inductance of the d-axis armature, Lq: the inductance of the q-axis armature, and r: the resistance of the d-axis armature and the q-axis armature.
According to the present invention, there is provided a motor control apparatus for converting a DC brushless motor into an equivalent circuit having a q-axis armature on a q-axis which is aligned with the direction of magnetic fluxes of field systems of the motor and a d-axis armature on a d-axis which extends perpendicularly to the q-axis, comprising current detecting means for detecting currents flowing through armatures of the motor, actual current calculating means for calculating a q-axis actual current flowing through the q-axis armature and a d-axis actual current flowing through the d-axis armature from the currents detected by the current detecting means, and current difference calculating means for calculating a q-axis current difference between a q-axis command current which is a command value for the current flowing through the q-axis armature and the q-axis actual current and a d-axis current difference between a d-axis command current which is a command value for the current flowing through the d-axis armature and the d-axis actual current, means for generating a d-axis command voltage which is a command value for the voltage applied to the d-axis armature and a q-axis command voltage which is a command value for the voltage applied to the q-axis armature in order to reduce the d-axis current difference and the q-axis current difference, and means for controlling the currents flowing through the armatures of the motor depending on the d-axis command voltage and the q-axis command voltage.
The motor control apparatus comprises proportional term component generating means for carrying out a proportional process to multiply the d-axis current difference and the q-axis current difference by respective predetermined proportional gains to generate a d-axis proportional term component which is a proportional term component of the d-axis command voltage and a q-axis proportional term component which is a proportional term component of the q-axis command voltage, integral term component generating means for effecting an integrating process on the d-axis current difference and the q-axis current difference based on a predetermined integral gain to generate a d-axis integral term component which is an integral term component of the d-axis command voltage and a q-axis integral term component which is an integral term component of the q-axis command voltage, and command voltage generating means for generating the d-axis command voltage depending on the sum of the d-axis proportional term component and the d-axis integral term component, and the q-axis command voltage depending on the sum of the q-axis proportional term component and the q-axis integral term component, means for setting the integral gain to stabilize a system in which the d-axis current difference and the q-axis current difference are multiplexed, integrated, and inputted, with respect to a steady gain which approximates, including the proportional gains, the steady input-to-output relationship of the motor to which the voltage applied to the d-axis armature and the voltage applied to the q-axis armature are inputted and from which the current flowing through the d-axis armature and the current flowing through the q-axis armature are outputted.
With the above arrangement, the proportional term component generating means generates the d-axis proportional term component and the q-axis proportional term component. In order to increase the ability of the d-axis actual current to follow the d-axis command current and the ability of the q-axis actual current to follow the q-axis command current to control the motor stably when the motor operates at a high rotational speed, it is necessary to increase the proportional gain thereby to increase the reaponse of the motor to the d-axis command voltage and the q-axis command voltage.
However, only increasing the proportional gain poses a problem in that the motor tends to vibrate in its operation. According to the present invention, therefore, the integral term component generating means generates the d-axis integral term component and the q-axis integral term component in order to alleviate the above shortcoming.
Specifically, the integral term component generating means performs the integrating process based on the integral gain that is set to stabilize the system in which the d-axis current difference and the q-axis current difference are multiplexed, integrated, and inputted, with respect to the steady gain which approximates, including the proportional gains, the steady input-to-output relationship between the voltage applied to the d-axis armature and the voltage applied to the q-axis armature and the current flowing through the d-axis armature and the current flowing through the q-axis armature, thereby generating the d-axis integral term component and the q-axis integral term component.
Stability of the integrating process using the steady gain will be described below with reference to FIG. 2(a). A steady gain M which approximates the input-to-output relationship of a system (2-input, 2-output system) to which a voltage Vd applied to a d-axis armature and a voltage Vq applied to a q-axis armature are inputted and from which a current Id flowing through the d-axis armature and a current Iq flowing through the q-axis armature are outputted, is multiplied by the difference xcex94Id between a command current value Id_c for the d-axis armature and the current Id and the difference xcex94Iq between a command current value Iq_c for the q-axis armature and the current Iq, and the products are integrated (Ki, 1/s) to generate a voltage Vd applied to the d-axis armature and a voltage Vq applied to the q-axis armature. In this case, variations in the differences xcex94Id, xcex94Iq are suppressed by the integrating process.
Therefore, if an integral gain Ki for stabilizing an output produced by multiplying the steady gain M by the current differences xcex94Id, xcex94Iq and integrating products is used, the system ranging from a subtractor 30 to the output of the steady gain M is stabilized as a whole, allowing the current Id to follow the command current value Id_c stably and also allowing the current Iq to follow the command current value Iq_c stably.
Thus, the integral term component generating means performs the integrating process based on the integral gain determined to stabilize the system based on the steady gain, thereby generating the d-axis integral term component and the q-axis integral term component. The d-axis command voltage is generated based on the sum of the d-axis integral term component and the d-axis proportional term component, and the q-axis command voltage is generated based on the sum of the q-axis integral term component and the q-axis proportional term component. In this manner, the system approximated by the steady gain is stabilized to control the motor stably with a good follow-up capability even when the motor operates at high rotational speeds.
Since the electric response of the motor is very quick, if the motor follows the d-axis command voltage and the q-axis command voltage at all times, then the steady gain in the steady state of the system can be expressed by the equation (3) shown below, and the input-to-output relationship can be expressed by the equation (4) shown below. The integral gain can be determined using the steady gain expressed by the equation (3).                     M        =                              [                                                                                r                    +                    Kp                                                                                                              -                      ω                                        ⁢                                          xe2x80x83                                        ⁢                    Lq                                                                                                                    ω                    ⁢                                          xe2x80x83                                        ⁢                    Ld                                                                                        r                    +                    Kp                                                                        ]                                -            1                                              (        3        )            
where M: the steady gain, r: the resistance of the d-axis armature and the q-axis armature, Kp: the proportional gains, Ld: the inductance of the d-axis armature, and Lq: the inductance of the q-axis armature;                               [                                                    Id                                                                    Iq                                              ]                =                                                            [                                                                                                    r                        +                        Kp                                                                                                                                      -                          ω                                                ⁢                                                  xe2x80x83                                                ⁢                        Lq                                                                                                                                                ω                        ⁢                                                  xe2x80x83                                                ⁢                        Ld                                                                                                            r                        +                        Kp                                                                                            ]                                            -                1                                      ⁡                          [                                                                    Vd                                                                                        Vq                                                              ]                                ≡                      M            ⁡                          [                                                                    Vd                                                                                        Vq                                                              ]                                                          (        4        )            
where Id: the current flowing through the d-axis armature, Iq: the current flowing through the q-axis armature, xcfx89: the angular velocity of the motor, Vd: the voltage applied to the d-axis armature, and Vq: the voltage applied to the q-axis armature.
Inasmuch as the steady gain M expressed by the equation (3) is a regular matrix, if the integral gain is established according to the equation (5) shown below using an arbitrary stable matrix S, then the state equation of an output (voltage) x according to an integrating process using the steady gain is indicated as the equation (6) shown below. The stable matrix is a matrix where the real parts of intrinsic values are all negative. If the system matrix (xe2x88x92KiM) in the equation (6) is a stable matrix, then the state of the output x according to the above state equation is stable.                     Ki        =                                                            -                                  det                  ⁢                  M                                            ·                              M                                  -                  1                                                      ⁢            S                    ≡                      (                                                            k11                                                  k12                                                                              k21                                                  k22                                                      )                                              (        5        )            
where Ki: the integral gain, and S: a predetermined arbitrary stable matrix.                                           ⅆ                          ⅆ              t                                ⁢          x                =                                            -              Ki                        ⁢                          xe2x80x83                        ⁢                          M              ·              x                                =                                    -              det                        ⁢                          xe2x80x83                        ⁢                          M              ·                              M                                  -                  1                                                      ⁢                          SM              ·              x                                                          (        6        )            
Since detM greater than 0 and Mxe2x88x921SM is a stable matrix in the equation (6), if the integral gain is determined according to the equation (5), then the system matrix (xe2x88x92KiM) is also stable matrix, stabilizing the state of the output x.
The integral term component generating means calculates the d-axis integral term component according to the equation (7) shown below and the q-axis integral term component according to the equation (8) shown below in the integrating process based on the integral gain.
Vdxe2x80x94i=∫(k11xc2x7xcex94Id+k12xc2x7xcex94Iq)dtxe2x80x83xe2x80x83(7)
Vqxe2x80x94i=∫(k21xc2x7xcex94Id+k22xc2x7xcex94Iq)dtxe2x80x83xe2x80x83(8)
where Vd_i: the d-axis integral term component, Vq_i: the q-axis integral term component, and k11, k12, k21, k22: matrix elements of the integral gain Ki defined by the equation (5).
If the integral gain is established according to the equation (9) shown below using an arbitrary positive definite matrix Q, then the state equation of an output (voltage) x according to an integrating process using the steady gain M expressed by the equation (3) is indicated as the equation (10) shown below. The positive definite matrix is a symmetrical real matrix where the intrinsic values are all positive. If the system matrix (xe2x88x92MTQM) in the equation (10) is a stable matrix, then the state of the output x is stable.                     Ki        =                                            M              T                        ⁢            Q                    ≡                      (                                                            k11                                                  k12                                                                              k21                                                  k22                                                      )                                              (        9        )            
where Q: a predetermined arbitrary positive definite matrix.                                           ⅆ                          ⅆ              t                                ⁢          x                =                                            -              Ki                        ⁢                          xe2x80x83                        ⁢                          M              ·              x                                =                                    -                              M                T                                      ⁢                          QM              ·              x                                                          (        10        )            
In the equation (10), because (MTQM) is a positive definite matrix, (xe2x88x92MTQM) is a stable matrix. Therefore, the state of the output x can be stabilized by determining the integral gain according to the equation (9).
The integral term component generating means calculates the d-axis integral term component according to the equation (7) and the q-axis integral term component according to the equation (8), using the integral gain Ki determined by the equation (9) in the integrating process based on the integral gain.
The above and other objects, features, and advantages of the present invention will become apparent from the following description when taken in conjunction with the accompanying drawings which illustrate preferred embodiments of the present invention by way of example.